I have done both GC and GA, so I feel I can give you a solid opinion.
GC: Propaganda provided outstanding GC tickets to the Hartford show I attended last June. The tickets were SO good that I felt I was out on the floor. Bono was "right there" as he walked by my seats on the ramp. Therefore, with good GC seats, the advantage is a great view possibly very close to the stage/ramp and you don't have to wait outside all day. You have an assigned seat, so if you need to leave for any reason, you won't lose your spot.
The disadvantage though is clearly the cost. The GC ticket is about 3x that of the GA (face values only). Also, you may get a bad GC ticket that puts you at the back of the GA area. Suddenly that's not such a great view. Therefore, before you buy any GC ticket, check where it is in the arena (most arenas are listed on the web, so you can identify the area).
GA: The GA ticket obviously allows you potential access inside the heart. This close proximity to the band is the appeal of the GA ticket.
Bono only pulls people with GA tickets onto the ramp, so again, this is a wonderful bonus for the fans with these tickets. If you get a spot at the tip of the heart (either inside or outside) you will literally be a few feet away from the band members as they perform. It's one thing to see them perform from a distance - it's another to see them perform literally right in front of you.
The disadvantage is that these are "hot" tickets. Therefore, your chances of getting one for the face value price of $45 is pretty slim (if you don't already have one). Be prepared to spend more on that GA ticket than you might if you just bought a GC ticket at face value. Also, to get the prime spots in the heart (right at the stage) or outside the heart (right at the tip) you need to wait outside in the GA line - sometimes all night. As you wrote, you don't have that type of time, so perhaps a GA ticket isn't the best choice for you. If you get in line at 5 p.m. you might still make the heart, but you won't get a good spot along the rail or be anywhere near the tip or the stage. Of course, you'll still be ridiculously close, but not the ideal spots fans like to be. Furthermore, as I wrote, if you don't have your GA ticket already, you may wind up paying a lot more than face value for it.
Another disadvantage is that without an assigned seat, even if you have a great spot, you can lose it if you have to leave the area (bathroom or drink breaks). The GC is great if you bought souvenirs and want to put them down on your seat as you enjoy the show - but with GA, you'll have to hold all souvenirs you may have bought before the concert.
Bottom line: GA provides the opportunity to be VERY close to the band and even pulled up on stage. But the price to pay is time (in the GA line) and now $$ (to the ticket broker for this "hot" ticket). GC provides the opportunity to have a great seat that's almost as good as a GA spot (and can be MUCH better) without having to wait in line all day. However, you won't be pulled up on stage with the GC ticket, and they are more expensive.
What do I recommend? Well, since you can't get there early, I say go for GOOD GC tickets. Considering how late you will arrive in the GA line, I'm guessing that you'll just get a spot outside the heart - not quite as special as you might have hoped. However, if you think you still have a chance of getting into the heart, even though you can't get into line until late, then get the GA.